The solution for polynomials p(x) + q(x) is 7x³ + 3x² + 7x + 5
Given,
The polynomials
p(x) = 1 + 2x + 3x²
q(x) = 4 + 5x + 7x³
We have to find the solution for p(x) + q(x)
Then,
p(x) + q(x) = (1 + 2x + 3x²) + ( 4 + 5x + 7x³)
p(x) + q(x) = 7x³ + 3x² + 2x + 5x + 1 + 5
p(x) + q(x) = 7x³ + 3x² + 7x + 5
That is,
The solution for polynomials p(x) + q(x) is 7x³ + 3x² + 7x + 5
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inserted a picture of the question, can you just answer the question and not ask a lot of questions yes i’m following
Step-by-step explanation:
A nonagon has 9 sides, so a regular nonagon will have vertices that are 40° apart as measured from the center. It has 9-fold rotational symmetry,
so the figure will be identical to the original when rotated multiples of 360°/9 = 40°.
[tex]\frac{360}{9}=40[/tex]Therefore the degrees will a nonagon have rotational symmetry
Hene the correct answer is Option B
NO LINKS!! Describe the domain and range (in BOTH interval and inequality notation) for each function shown part 1a
Answer:
Domain as an inequality: [tex]\boldsymbol{\text{x} < 6 \ \text{ or } \ -\infty < \text{x} < 6}[/tex]
Domain in interval notation: [tex]\boldsymbol{(-\infty, 6)}[/tex]
Range as an inequality: [tex]\boldsymbol{\text{y} \le 6 \ \text{ or } \ -\infty < \text{y} \le 6}[/tex]
Range in interval notation: [tex]\boldsymbol{(-\infty, 6]}[/tex]
=========================================================
Explanation:
The domain is the set of allowed x inputs. For this graph, the right-most point is when x = 6. This endpoint is not part of the domain due to the open hole. The graph goes forever to the left to indicate [tex]\text{x} < 6[/tex] but I think [tex]-\infty < \text{x} < 6[/tex] is far more descriptive.
The second format directly leads to the interval notation of [tex](-\infty, 6)[/tex]
Always use parenthesis for either infinity. We use a parenthesis for the 6 to tell the reader not to include it as part of the domain.
------------------------
The range is the set of possible y outputs.
The highest y can get is y = 6
Therefore, y = 6 or y < 6
The range can be described as [tex]\text{y} \le 6 \ \text{ or } \ -\infty < \text{y} \le 6[/tex] where the second format is better suited to lead directly to the interval notation [tex](-\infty, 6][/tex]
Use a square bracket to include the 6 as part of the range. We don't have any open holes at the peak mountain point.
Answer:
[tex]\textsf{Domain}: \quad (-\infty, 6) \quad -\infty < x < 6[/tex]
[tex]\textsf{Range}: \quad (-\infty,6] \quad -\infty < y\leq 6[/tex]
Step-by-step explanation:
The domain of a function is the set of all possible input values (x-values).
The range of a function is the set of all possible output values (y-values).
An open circle indicates the value is not included in the interval.
A closed circle indicates the value is included in the interval.
An arrow show that the function continues indefinitely in that direction.
Interval notation
( or ) : Use parentheses to indicate that the endpoint is excluded.[ or ] : Use square brackets to indicate that the endpoint is included.Inequality notation
< means "less than".> means "more than".≤ means "less than or equal to".≥ means "more than or equal to".From inspection of the given graph, the function is not continuous and so the domain is restricted.
There is an open circle at x = 6.
Therefore, the domain of the function is:
Interval notation: (-∞, 6)Inequality notation: -∞ < x < 6From inspection of the given graph, the maximum value of y is 6.
The function continues indefinitely to negative infinity.
Therefore, the range of the function is:
Interval notation: (-∞, 6]Inequality notation: -∞ < y ≤ 698) Cost to store: $145Markup: _?Selling price:$319.
Answer: Mark up is 220%
Cost to store : $145
selling price = $319
let x = mark up
Using the below equation
[tex]\begin{gathered} \text{Part = whole x percentage} \\ \text{part = selling price} \\ \cos t\text{ to store = whole} \\ \text{Mark up = percentage} \\ 319\text{ = 145 }\cdot\text{ x\%} \\ \text{ x\% = }\frac{319}{145}\text{ x 100\%} \\ x\text{ = 2.2 x 100\%} \\ x\text{ = 220\%} \\ \text{Therefore, the mark up is 220\%} \end{gathered}[/tex]Ethan found the spinner shownbelow and planned to use it for agame.2332453235After studying the spinner beforeusing it, Ethan correctly concludedthat the spinner was-A least likely to land on 2B least likely to land on 5C most likely to land on 3D most likely to land on 2
we have that
the number 3 appears 4 times
so
answer is
option C most likely to land on 3
Describe in words where the square root of 60 minus 11 would be plotted on a number line.
Answer:
it would be on 7 since 60-11=49 and the square root of 49 is 7
Find the zero for the polynomial function and give the multiplicity for each zero. State whether the graph crosses to x axis or touch the x axis and turn around, at each zero.
we have the function
f(x)=2(x-6)(x-7)^2
REmember that the zeros of the function are the values of x when the value of the function is equal to zero
In this problem
the zeros of the function are
x=6 -------> multiplicity 1 (the graph crosses to x axis)
x=7 ----- multiplicity 2 (touch the x axis and turn around)
see the attached figure to better understand the problem
I'm not sure how to do this. This is a long one that's why.
We have the following:
For the area surface:
[tex]As=2\pi rh[/tex]repacing:
r = 1.5 in
h = 7 in
[tex]\begin{gathered} As=2\cdot3.14\cdot1.5^{}\cdot7 \\ As=65.94 \end{gathered}[/tex]The answer is 65.9 in^2
For volume:
[tex]\begin{gathered} V=\pi r^2h \\ V=3.14\cdot1.5^2\cdot7 \\ V=49.455 \end{gathered}[/tex]The answer is 49.5 in^3
two slices of dans famous pizza have 230 calories how many calories would you expect to be in 5 slices of pizza
We can answer this question, using proportions. We can see it graphically as follows:
Then, we have that 5 slices will have 575 calories.
A person chooses a number in a set containing the first 5 cubic numbers. Find the set representing the event E of choosing a number that can be evenly divided by 2. Give your answer as a set, e.g. {1,2,3}, using the cubed number (not the base number) and do not include E= in your answer.
The first 5 cubic numbers are:
[tex]\lbrace1,8,27,64,125\rbrace[/tex]To find the set that represents event E we have to choose the numbers from the set above that are evenly divided by 2; this means that we have to choose the numbers that are multiple of 2. We notice that this numbers are 8 and 64, therefore the set that represents event E is:
[tex]\lbrace8,64\rbrace[/tex]add or subtract : x/4 + 3/4 =
Answer:
x + 3 / 4
Explanation:
Write the equation of the line that passes through the points (12, 4) and (22,9).
Given the following points that pass through the line:
Point A : 12,4
Point B : 22,9
Step 1: Let's determine the slope of the line (m).
[tex]\text{ m = }\frac{y_2-y_1}{x_2-x_1}[/tex][tex]\text{ = }\frac{9\text{ - 4}}{22\text{ - 12}}[/tex][tex]\text{ m = }\frac{5}{10}\text{ = }\frac{1}{2}[/tex]Step 2: Let's determine the y-intercept (b). Substitute m = 1/2 and x,y = 12,4 in y = mx + b.
[tex]\text{ y = mx + b}[/tex][tex]\text{ 4 = (}\frac{1}{2})(12)\text{ + b }\rightarrow\text{ 4 = }\frac{12}{2}\text{ + b}[/tex][tex]\text{ 4 = 6 + b}[/tex][tex]4\text{ - 6 = b}[/tex][tex]\text{ -2 = b}[/tex]Step 3: Let's complete the equation. Substitute m = 1/2 and b = -2 in y = mx + b.
[tex]\text{ y = mx + b}[/tex][tex]\text{ y = (}\frac{1}{2})x\text{ + (-2)}[/tex][tex]\text{ y = }\frac{1}{2}x\text{ - 2}[/tex]Therefore, the equation of the line is y = 1/2x - 2.
The coordinates of triangle LMN are shown.YL(-1,4)XN (4, -1)M(-1, -3)What is the length of LM? Enter the answer in the box.unit(s)
Given data:
The given coordinate of L is (-1,4).
The given coordinate of M is(-1, -3).
The expression for LM length is,
[tex]\begin{gathered} LM=\sqrt[]{(-1-(-1))^2+(-3-4)^2} \\ =\sqrt[]{0+49} \\ =7 \end{gathered}[/tex]Thus, the LM length is 7 units.
fill in the table using the function rule y= 6x-3
Answer:
-9,-3,3,27
Step-by-step explanation:
Just multiply x by 6 and subtract 3 to that
Solve the Equation , I tried multiplying that 6 to the numbers in the parentheses but i couldnt get it
To start we will do what you said, multiply the 6, so:
6*(n-4)=3n
6n-6*4=3n
6n-24=3n
6n=3n+24
6n-3n=24
3n=24
n=24/3
n=8
So the answer is: 8
After reading the question what would the inequality equation and the graph shade look like?
It is given that the one number is always less than the opposite of the other.
So the equation formed is y<-x
The graph is obtained as
11) -3(1 + 6r) = 14 - r 12) 660+6)-5=1+6v 13) -4k + 2(5k - 6) = -3k - 39 14) -16 + 5n=-71-
-3(1+6r) = 14 -r
-3-18r = 14 - r
-3-14 = -r +18r
-17 = 17r
17r/17 = -17/17
r = -1
distributive property 3x(7x+6)
By distributive property, we distribute 3x, and multiply it to each term inside the binomial (7x+6) accounting for the sign.
[tex]\begin{gathered} 3x(7x+6) \\ \Rightarrow3x(7x)+3x(6) \\ \Rightarrow21x^2+18x \\ \\ \text{Therefore, }3x(7x+6)=21x^2+18x \end{gathered}[/tex]cos2 0-cos 20 = sin2 0
According to Double identities
[tex]\cos (2x)=2cos^2(x)-1[/tex][tex]\begin{gathered} \cos ^2(x)-sen^2(x)=2\cos ^2(x)-1 \\ -sen^2(x)=2\cos ^2(x)-\cos ^2(x)-1 \\ -sen^2(x)=\cos ^2(x)-1 \\ 1=\cos ^2(x)+sen^2(x) \end{gathered}[/tex]3. Darren won Round 3 of the game. Sherri is wondering if she lost Round 3 by 5 points or by 25 points. Explain to Sherri how many points Darren won Round3 by and show the mathematics you used to justify your answer.4. Sherri and Darren actually played with a third player, their friend Eric. Unfortunately, Eric forgot to record the points he scored in each of the three roundsin the table.
Sherry lost the round 3 by 25 points
Explanation:Sherry's point in third round = -10
Darren's point in the third round = 15
To determine the number of points Sherry lost round 3 by, we will subtracct Sherry's point from Darren's point:
[tex]\begin{gathered} \text{Darren's point - Sherry's point} \\ =\text{ 15 - (-10)} \\ =\text{ 15 + 10} \\ =\text{ 25} \end{gathered}[/tex]Sherry lost round 3 by 25 points
shirts are 15% off. The original price of one shirt is $20. What is the total cost, in dollars, of a shirt, at the sales price, including a 10% sales tax?
The original price of the shirt is , 20 dollar.
It is given that the shirts are 15% off.
Therefore, the price of the shirt is ,
[tex]20-20\times\frac{15}{100}=17.[/tex]The price of the shirt is, 17 dollar after 15% off.
It is also given that there are 10% sales tax.
The total cost of the shirt is determined by including the sales tax in the price of the shirt after 15% off.
[tex]17+(17\times\frac{10}{100})=18.7[/tex]Thus, The total cost of shirt is calculated as, 18.7 dollar.
how do i solve (4x^3 + 2x - 3) divided by (x - 3) with long division??
We want to divide 4x³ + 2x - 3 by x - 3 with the long division method
First, we rewrite the polynomial as:
4x³ + 0x² + 2x - 3
Them we divide the first term of the dividend by the highest term of the divisor:
4x²
x - 3 |4x³ + 0x² + 2x - 3
Then we multiply the divisor by this result:
| 4x²
x - 3 |4x³ + 0x² + 2x - 3
4x³ - 12x²
Now we subtract this result from the dividend:
| 4x²
x - 3 |4x³ + 0x² + 2x - 3
4x³ - 12x²
|12x² + 2x - 3
Now we can repeat all the previous steps using the last result as dividend:
| 4x² + 12x
x - 3 | 12x² + 2x - 3
12x² - 36x
|38x - 3
And we repeat these steps once more:
4x² + 12x + 38
x - 3 | 38x - 3
34x - 102
|99
The final term is the remainder
Then, we have:
4x³ + 2x - 3 = (x - 3)*(4x² + 12x + 34) + 99
Find the measurement of each side indicated and round to the nearest tenth for both triangles
a) We have a right triangle.
We have to find the value of x, which is the hypotenuse.
We can relate the angle B, the side AC and x with a trigonometric ratio as:
[tex]\begin{gathered} \sin (B)=\frac{\text{Opposite}}{\text{Hypotenuse}}=\frac{AC}{AB} \\ \sin (57\degree)=\frac{10.8}{x} \\ x=\frac{10.8}{\sin (57\degree)} \\ x\approx\frac{10.8}{0.83867} \\ x\approx12.9 \end{gathered}[/tex]b) In this case, x is the adyacent side to angle A.
We can relate the sides and the angle as:
[tex]\begin{gathered} \cos (A)=\frac{\text{Adyacent}}{\text{Hypotenuse}}=\frac{AC}{AB} \\ \cos (47\degree)=\frac{x}{3} \\ x=3\cdot\cos (47\degree) \\ x\approx3\cdot0.682 \\ x\approx2.0 \end{gathered}[/tex]Answer:
a) x = 12.9
b) x = 2.0
Select the correct answer..What is the value of i^ if the remainder of 4 is 2?OA. -i'OB.-1Ос. іOD. 1ResetNext
1) Considering that for that complex number we have the following pattern:
[tex]\begin{gathered} i^1=i \\ i^2=-1 \\ i^3=-1\cdot i=-i \\ i^4=-1\cdot-1=1 \end{gathered}[/tex]2) And that, the question asks us about the what number must be that exponent so that the remainder is 2, we can write out:
[tex]\frac{n}{4}=4d+2[/tex]which d is the divisor, so if the remainder is 2 then we can state:
[tex]i^n=i^2=-1[/tex]Given sin(x)=.4 and cot(x) >0 what is cos(x)?
The cotangent is given by the cosine over the sine.
If the cotangent is positive and the sine is positive, that means the cosine is also positive.
Now, in order to find the value of cos(x), we can use the following property:
[tex]\begin{gathered} \sin ^2(x)+\cos ^2(x)=1 \\ (0.4)^2+\cos ^2(x)=1 \\ 0.16+\cos ^2(x)=1 \\ \cos ^2(x)=1-0.16 \\ \cos ^2(x)=0.84 \\ \cos (x)=0.917 \end{gathered}[/tex]What is the equation of the following graph?A. f(x) = 2(3*)OB. f(x) = (4)Oc. f(x) = 3(2)D. f(x) = 5(2") y
Given
The graph,
To find:
The equation representing the given graph.
Explanation:
It is given that,
That implies,
From the given graph,
It is clear that the curve passes through, (0,5).
Then, for x=0,
Consider the equation,
[tex]\begin{gathered} f(0)=5(2^0) \\ =5\times1 \\ =5 \end{gathered}[/tex]Which is equal to y=5.
Hence, the equation representing the above graph is,
[tex]f(x)=5(2^x)[/tex]For which values of A, B, and C will Ax + By = C be a horizontal line through the point (−4, 2)?
The set of values {A = 0, B = 1, and C = 2} to have a completely horizontal line.
What is a horizontal line?A horizontal line is defined as a line with slope m = 0 that is parallel to the x-axis.
A horizontal line across (-4,2) informs us of two things.
A horizontal line with slope m = 0 is parallel to the x-axis.
The line crosses the point (-4,2).
Ax + By = C has m = B/A = 0 slope and intersects point (-4,2).
Then, B = A×0 indicates that any constant A will work, and the Ax term disappears.
Ax + By = C then becomes y = C. To find C, use the point (-4,2).
⇒ C = 2
This line's equation is y = 2, and any point (x,2) matches the equation.
Therefore, the set of values {A = 0, B = 1, and C = 2} to have a completely horizontal line.
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Answer:
Step-by-step explanation:
17
2. Write a story that can be represented by the equation y = x + 1/4 x.Question 2 On a hot day a football team drank an entire 50-gallon cooler of water and half as much again. How much water did they drink? Create an equation to represent this situation.
y= x+ 1/4 x
Y = dependent variable
x= independent variable
Jenny has a bank account. In the first month, she deposits a certain amount of money (x), and in the month after she deposits 1/4 of that amount.
Find the total amount of money deposited (y).
Jackson started a savings account using the bonus he received from work of $3,500. Theaccount is compounded weekly with an interest rate of 1.75% How much interest did theaccount earned in 18 years?O $1,295.65O $1,102.500 $4,795.65o $1,290
The amount compounded is given by the formula ;
[tex]A=P\lbrack1+\frac{r}{100n}\rbrack^{nt}[/tex]Here, P = $3500, r = 1.75%, n = 52 , t = 18 years.
[tex]\begin{gathered} A=3500\lbrack1+\frac{1.75}{100\times52}\rbrack^{52\times18} \\ A=4795.65 \end{gathered}[/tex]Therefore, the interest the account will earn is 4795.65-3500 = $1295.65, Option A
Use the following function rule to find (2). f(x) = (-5 - 2x)? ? f(2) = | Submit
To find f(2) you subtitute the value of x in the function by 2:
[tex]f(2)=-5-2(2)[/tex][tex]f(2)=-5-4[/tex][tex]f(2)=-9[/tex]Then, f(2) is -9A line passes through the points (7,9) and (10,1). What is its equation in point-slope form?
Use one of the specified points in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
Answer:
[tex](y - 9) = (-8/3)\, (x - 7)[/tex].
Step-by-step explanation:
If a line in a cartesian plane has slope [tex]m[/tex], and the point [tex](x_{0},\, y_{0})[/tex] is on this line, then the point-slope equation of this line will be [tex](y - y_{0}) = m\, (x - x_{0})[/tex].
The slope of a line measures the rate of change in [tex]y[/tex]-coordinates relative to the change in the [tex]x[/tex]-coordinates. If a line goes through two points [tex](x_{0},\, y_{0})[/tex] and [tex](x_{1},\, y_{1})[/tex], the slope of that line will be:
[tex]\begin{aligned}m &= \frac{y_{1} - y_{0}}{x_{1} - x_{0}}\end{aligned}[/tex].
In this question, the two points on this line are [tex](7,\, 9)[/tex] and [tex](10,\, 1)[/tex], such that [tex]x_{0} = 7[/tex], [tex]y_{0} = 9[/tex], [tex]x_{1} = 10[/tex], and [tex]y_{1} = 1[/tex]. Substitute these values into the equation to find the slope of this line:
[tex]\begin{aligned}m &= \frac{y_{1} - y_{0}}{x_{1} - x_{0}} \\ &= \frac{1 - 9}{10 - 7} \\ &= \left(-\frac{8}{3}\right)\end{aligned}[/tex].
With the point [tex](7,\, 9)[/tex] as the specific point [tex](x_{0},\, y_{0})[/tex] (such that [tex]x_{0} = 7[/tex] and [tex]y_{0} = 1[/tex]) as well as a slope of [tex]m = (-8 / 3)[/tex], the point-slope equation of this line will be:
[tex]y - y_{0} = m\, (x - x_{0})[/tex].
[tex]\displaystyle y - 9 = \left(-\frac{8}{3}\right)\, (x - 7)[/tex].